A diagram made by cutting open the surface of a solid and spreading it out on a plane is called a net. Folding the net produces the original solid.
Nets of Prisms and Cylinders
A net of a prism consists of two bases (polygons) and several lateral faces (rectangles). When the lateral surface of a cylinder is unfolded, it becomes a rectangle (vertical = height, horizontal = circumference of the circular base).
📘 Example ①
For a cylinder with a base radius of 3 cm and a height of 5 cm, find the vertical and horizontal lengths of the rectangle representing its lateral surface.
Answer: Vertical = height = 5 cm. Horizontal = circumference of the circular base = 2π×3 = 6π cm
For a cylinder with a base radius of 3 cm and a height of 5 cm, find the vertical and horizontal lengths of the rectangle representing its lateral surface.
Answer: Vertical = height = 5 cm. Horizontal = circumference of the circular base = 2π×3 = 6π cm
Nets of Pyramids and Cones
In a net of a cone, the lateral surface becomes a sector. The length of the arc of the sector = circumference of the circular base.
💡 Key Points
- Lateral surface of a cylinder: a rectangle with vertical=height and horizontal=circumference of the circular base (2πr)
- Lateral surface of a cone: a sector (arc=circumference of the circular base)
- When a net is assembled, the edges fit together exactly
Practice Problem
- Find the area of the net of the lateral surface (rectangle) of a cylinder with a base radius of 2 cm and a height of 4 cm.
Answer and Explanation
- Answer: 16π cm². Vertical=4, horizontal=2π×2=4π. Area=4×4π=16π.